Your example is not parallel construction either. If you hear that Joe has coke in his car you already have probable cause to search Joe's car. You don't need t

Your example is not parallel construction either. If you hear that Joe has coke in his car you already have probable cause to search Joe's car. You don't need to wait until he speeds, since speeding wouldn't give you a reason to search his vehicle. Parallel construction would be: you pulled Joe over for [whatever reason] and searched his car without probable cause (maybe he seemed shifty or he was being a dick) and found coke, so you subsequently went to an informant who told you that he witnessed Joe selling coke out of his car earlier on the day of the search (which would have given you probable cause to search his car if you had talked to the informant before pulling Joe over). The basis of parallel construction is that a real investigation would have uncovered the evidence anyway. What many people don't get is that law enforcement actually has to do the legwork of a real investigation (but knowing what to look for, and where, etc.) to show that the excluded evidence should be made admissible. It's a remedy for law enforcement to cure procedural violations of due process under the Fourth Amendment.